The authors studied cylindrical detonation (CD) induced by a direct initiation in the hydrogen/oxygen gas mixture using the 2-dimensional compressible Euler equations with a detailed chemical reaction model. As the result, a cellular structure of cylindrical detonation is obtained in the maximum pressure histories such as an open-shutter photograph and a smoked-foil record in the experimental results. The influence of the initiation energy on the propagation of cylindrical detonation is studied to obtain the subcritical and supercritical regimes: The generation of new transverse wave is observed and small cells during their propagation appear just after the detonation initiation. Furthermore, the number of transverse waves increases nonlinearly near the detonation front in each condition. The generation rate of the transverse wave under the high initiation energy becomes slow because the overdriven state which produces a strong shock wave is maintained longer than that under the low initiation energy.